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I didn't mean to be pussy. After you have read this thread, I believe you understand why I had to ask if this is a question or a statement.

Most of all. It doesn't sound redundant to me. Each of them has their own feeling to me. But the problem is how they are different. Unfortunatly, it's difficult to explain it.
It seems like trying to explain the difference between 'a' , 'the', and 'zero articles' or between 'I like to ski.' and 'I like skiing'. There is certainly some difference , which sometimes is not important, but sometimes could be very critical as to bring about misunderstandings. Anyway, let me have a try.

In the example you gave us, 제주도에 refers to only the fact that 제주도 has a mountain to my ear. In contrast, 제주도에는 implies to me that compared to other places, specially 제주도 has a mountain or 제주도 should have a (special) mountain unlike other places. -에는 gives me a feeling that I have to focus on the noun that 에는 helps, so I have got a feeling of a expectation as kind of a subjuctive mood that there should or would be a special mountain in 제주도, unlike other places.

철수는 밥을 먹는다. (It could imply other guys aren't eating something, and unlike them, 철수 is eating his meal.)
철수가 밥을 먹는다. (From this we don't know if others eat their meal or not. From it we can know just the fact that 철수 is eating something.)

If you ask to people living in 제주도 '제주도에 산이 있습니까?', you just ask about the fact whether 제주도 has a mountain. But if you asked them '제주도에는 산이 있습니까?", you could sound to mean though you don't want to believe 제주도 has a mountain, you would just try asking about it. Although I am not be able to translate it into Englisn well with my poor English, it could be sound as if 'Is there a mountain in 제주도 at all?'

I'm sure there are so many other aspects of '-는' or '-에는' this thread so far hasn't dealt with. As there is no single general rule to explain the differences of articles in Enlgish, I think it is difficult to find out one single effective explanation about the way to distinguish '-에' and '-에는'. Nonetheless, I hope this make any help.